Sears has identified 505 stores — including 11 in Illinois — the bankrupt retailer hopes to sell to a new owner that would continue operating them.

The stores, which include Sears locations in Bloomingdale, Chicago Ridge, North Riverside, Oak Brook, Schaumburg, West Dundee, Cherry Valley, Peoria and Fairview Heights and Kmarts in Bridgeview and Des Plaines, were identified late Wednesday in a Bankruptcy Court filing.

Hoffman Estates-based Sears Holdings Corp., which filed for Chapter 11 bankruptcy protection in mid-October, received court approval last week to begin trying to sell its best-performing stores. The retailer earlier received court approval to begin store closing sales at 142 unprofitable stores, including a Sears in Joliet and Kmart stores in Moline, Quincy and Norridge.

Sears has until Dec. 15 to find an initial bidder, or “stalking horse,” for the stores it hopes to keep open. Other potential buyers have until Dec. 28 to submit bids, and the auction will be conducted Jan. 14.

ESL Investments, the hedge fund run by Sears Chairman Edward Lampert, had been in talks with the company about buying a large group of stores. At a court hearing last month, an attorney for Sears said ESL was a “likely bidder.”

While Sears hopes to find a buyer that would continue operating the retail business, it also is accepting bids from buyers that would liquidate, according to a letter from Lazard, the firm handling the auction process for the retailer.